The inherent resolution of digital cameras known in the art, such as cameras based on CCD or CMOS sensor arrays, is generally limited by the resolution of the sensor array itself. In order to avoid degrading resolution still further, the objective optics used in such cameras are typically designed so that the optical point spread function (PSF) has an extent smaller than the pitch of the array. In other words, the optics are designed so that a bright point in the object plane is imaged to a spot no more than one pixel in size on the sensor array.
The PSF of an optical system may vary from the ideal due to focal variations and aberrations. A number of methods are known in the art for measuring and compensating for such PSF deviations by digital image processing. For example, U.S. Pat. No. 6,154,574, whose disclosure is incorporated herein by reference, describes a method for digitally focusing an out-of-focus image in an image processing system. A mean step response is obtained by dividing a defocused image into sub-images, and calculating step responses with respect to the edge direction in each sub-image. The mean step response is used. in calculating PSF coefficients, which are applied in turn to determine an image restoration transfer function. An in-focus image is obtained by multiplying this function by the out-of-focus image in the frequency domain.
As another example, U.S. Pat. No. 6,567,570, whose disclosure is incorporated herein by reference, describes an image scanner, which uses targets within the scanner to make internal 30 measurements of the PSF. These measurements are used in computing convolution kernels, which are applied to images captured by the scanner in order to partially compensate for imperfections of the scanner lens system.
It is also possible to add a special-purpose blur to an image so as to create invariance to certain optical aberrations. Signal processing is then used to remove the blur. A technique of this sort is described by Kubala et al., in “Reducing Complexity in Computational Imaging Systems,” Optics Express 11 (2003), pages 2102-2108, which is incorporated herein by reference. The authors refer to this technique as “Wavefront Coding.” A special a spheric optical element is used to create the blur in the image. This optical element may be a separate stand-alone element, or it may be integrated into one or more of the lenses in the optical system. Optical designs and methods of image processing based on Wavefront Coding of this sort are described, for example, in U.S. Pat. No. 5,748,371 and in U.S. Patent Application Publications US 2002/0118457 A1, US 2003/0057353 A1 and US 2003/0169944 A1, whose disclosures are incorporated herein by reference.